How to occlude objects at a far distance?

I have a big virtual environment with some pillars.  Currently, the AR objects are being rendered over the pillars.  I would like a way to occlude the objects where the physical pillars are so that the virtual objects appear to be behind the pillars.

In the HoloLens and Magic Leap, I would simply include the virtual pillars and put a matte black material on them.  The headset would render the black objects (the virtual pillars) as passthrough, and occlude any virtual object behind them, thereby making the virtual objects appear to be behind the physical pillars.

How do I do something similar with the Quest 3?  When I research this topic, the solution seems to be use Depth API, but my virtual environment is much too large for that solution.  How do I get a virtual object to appear behind a physical object that is far away? 

Thanks.